New Scientist letters: Not so Fibonacci
From Ian Stewart Coventry, Warwickshire, UK:
Gael Mariani and Martin Scott perpetuate a series of myths in their letter about Fibonacci numbers in nature (3 September, p 19). It is true that the Fibonacci numbers are associated with a particular kind of spiral - the logarithmic spiral - and they are also closely associated with the "golden number", which is roughly 1.6. And the nautilus shell does have the form of a logarithmic spiral.
Unfortunately the correlation ends there, because there are many different logarithmic spirals. In such spirals the space between consecutive windings grows exponentially at a fixed rate, and this rate can be any positive number. The usual "Fibonacci" spiral has a growth rate of about 6.8 - the fourth power of the golden number - whereas that of the nautilus is about 3, meaning it is too tightly wound to be related to Fibonacci. This growth rate is different in different gastropod species.
The spirals in horns have even less to do with Fibonacci. The connection with elephant tusks is pretty much non-existent. The spirals of galaxies are not even logarithmic. In particular, most have two arms winding from the centre, whereas the logarithmic spiral has a single arm.
The connection between Fibonacci numbers, certain spirals, the golden number and the structure of many plants is genuine and increasingly well understood. Most other alleged occurrences of Fibonacci in nature are bogus.
A great example of people getting carried away by an interesting phenomenon.
Fitz did a great cartoon about Fibonacci spirals in snail shells many years ago. I must ask him if he still has a copy—but only maths anoraks will appreciate it.
Talking of obscure mathematical cartoons, see also: Challenge